Communications in Number Theory and Physics

Volume 10 (2016)

Number 3

Monstrous BPS-algebras and the superstring origin of moonshine

Pages: 433 – 526

DOI: http://dx.doi.org/10.4310/CNTP.2016.v10.n3.a2

Authors

Natalie M. Paquette (Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, California, U.S.A.)

Daniel Persson (Department of Physics, Chalmers University of Technology, Gothenburg, Sweden)

Roberto Volpato (Theory Group, SLAC National Accelerator Laboratory, Menlo Park, California, U.S.A.; and Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, Calif., U.S.A.)

Abstract

We provide a physics derivation of Monstrous moonshine. We show that the McKay–Thompson series $T_g, g \in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models. The invariance groups of these series arise naturally as spacetime T-duality groups and their genus zero property descends from the behaviour of these heterotic models in suitable decompactification limits. We also show that the space of BPS-states forms a module for the Monstrous Lie algebras $\mathfrak{m}_g$, constructed by Borcherds and Carnahan. We argue that $\mathfrak{m}_g$ arise in the heterotic models as algebras of spontaneously broken gauge symmetries, whose generators are in exact correspondence with BPS-states. This gives mg an interpretation as a kind of BPS-algebra.

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Published 15 November 2016